A dog gives a look like it's nothing,
And pleasantly, though injured, it bow wows
Today's a rainy day,
A rainy day

The girl in tears up on the roof,
She licked on a candy apple and looked to the sky
Today's a rainy day,
A rainy day

Holding my lantern, singing out,
It's time to get set for tomorrow
Now to chant the words of praise:
C'mon, hyneri lanla!

Singing with a fish's face,
Jumping over the barbed wire
Let's play now; let's laugh now!

Singing of my silly little love all throughout this town
Once the lights are lit, there's nothing there
One, two, three, four, five, on the signal, that's when I go to meet you
Off to go pick up a brand new light!

Even names have been forgotten
The payphone goes huff puff
Today's still a rainy day,
A rainy day

Surrounded with cigarette smoke,
We choked it down and walked down the back alleys
A rainy day,
A rainy day

When the antenna's up, is it alright?
Popping my head out from the shopping district,
To the crying child, I chant:
C'mon, hyneri lanla!

Full of nothing but goodbyes,
Shrink away the self-contradictions
Don't cry, don't falter...

With this globe spinning in my right hand,
Shall I brighten it up with the light in my left?
That moment the sky changed its color,
Deep in me, you were what remained

In the rain shelter of the candy shop,
I awaited God's return
So, shall we sing? The sheep's song!
With that lantern in your hands,
Illuminate everything, so like the sun...

You sing the song all throughout this town
Lighting the light, and it's a wondrous thing
One, two, three, four, five, on the signal, that's when I go to meet you
Off to go pick up a brand new light!

What's at the end of the tunnel?
I'm stepping forth out of the town
One, two, three, four, five, on the signal, that's when I go to meet you
Off to go pick up a brand new light!

Down on the ground, the dog's acting like it's nothing
It's injured, but it's glad, it's glad to bow wow out
Today... rainy day,
Rainy day

Sobbing girl up on the roof, once she's done crying her eyes out,
She licked her candy apple and then looked into the sky
Today... rainy day,
Rainy day

Even with a fish face, sing a song
Jump the barbed wire, and head right along
Let's play today; let's laugh all day!

Singing my little love to everyone all throughout this town
And yet once the lights are lit, there's nothing at all
One, two, three, four, five, on the signal, that's when I go meet you
Now then, I'll be off to find a brand new light!

Who knows for sure, maybe their names were forgotten
The payphone makes a sound, it's ringing huff puff tones
And still... rainy day,
Rainy day

Cigarettes surround us and we're smogged down, it's smoky,
We choked it down, down back alleys, we had to proceed on our way
Rainy day,
Rainy day

When the antenna's up, then it's fine?
From the plaza, I come right on out
Hey, don't you cry, child, hear me shout:
C'mon, hyneri lanla!

Holding in my right hand this endlessly revolving globe,
What say that I brighten it with my left's light?
When the sky changed color, I know exactly what I thought:
Somewhere, deep inside of me, what remained was you

In the candy shop, sheltered from the rain,
Hoping for God's return, I awaited
So, shall we sing it? The sheep's song, understand!
With that lantern swinging along with your hands,
Like the sun, shine on all things in the land...

Now you sing out my song to everyone throughout this town
And yes, when the lights are lit, it's such a wondrous thing
One, two, three, four, five, on the signal, that's when I go meet you
Now then, I'll be off to find a brand new light!

Heading out the tunnel, and what awaits us at its end?
Finally, it's time to step forth out of the town
One, two, three, four, five, on the signal, that's when I go meet you
Now then, I'll be off to find a brand new light!

"Don't give up and say "I don't get it" - if you put in the effort to come up with your own meaning, can't you enjoy it more?" - Hachi
It should also be noted that Hachi has long had an appreciation for the varying interpretations of Studio Ghibli's works and a desire to create something like them, which clearly took form in this song.
* I SAID I WANT A PRETENTIOUS ANALYSIS

The main theme is simply bringing happiness (or as it typically is in the song, "light") to others.
Wander keeps remarking that it's a "rainy day" - though obviously being non-literal, since it's perfectly clear - but that puts no damper on their mood.
Of course, this is why they have a sheep and "sing the sheep's song": because they're both totally innocent.
The masked guys come off as outcasts, but Wander accepts them for who they are, even ending up entrusting the lantern to one.
The masked look-alike could be Wander's long-lost sister or something... except "here, hold this, bye forever" is an awfully weird reunion.
More likely, since their masks are probably a No-Face reference, she's a "Same-Face" that was able to copy Wander's face, which perhaps suggested to Wander that she could handle their lantern duty.
"Full of goodbyes" may relate in some way to the shrine; something along the lines of people only turning to the heavens in bad times.
Wander might not quite be an exception, though, seeing as they "awaited God" while supposedly sheltering from "rainy days." Of course, they're never visibly sad about the "rain."
Alternatively, uh... what if Wander IS "God" (or, you know, the sun goddess Amaterasu) because they brightened up the globe, and Same-Face is singing that part?
Whatever the globe may actually be, it makes it pretty clear that Wander's hope is to brighten up the whole world, not just Wonderland, which is why they leave (but leave the look-alike "in charge" of Wonderland).
The giant black cat of ill omen represents a gloom over the town, which disappears by the end. Hooray!
(And by all that, I mean Wonderland is heaven and Wandersheep is the cutest little Christ figure.)
(And by THAT, I mean Wander was sent by the black cat of ill Dormin omen to light up Wonderland in exchange for the cat reviving their dead girlfriend, Mono Same-Face.)
Oh, and on a pretty much unrelated note, I think the main reason Hachi said "rainy day" in English instead of "ame no hi" was because "hi" could be "day" or "light," and I think he wanted to keep those things separate.
Or at the very least, light and rainy days, because "Off to go meet a brand new day!" makes a lot of sense as well.